Question: Solve for $x$ : $6x^2 - 78x + 216 = 0$
Explanation: Dividing both sides by $6$ gives: $ x^2 {-13}x + {36} = 0 $ The coefficient on the $x$ term is $-13$ and the constant term is $36$ , so we need to find two numbers that add up to $-13$ and multiply to $36$ The two numbers $-4$ and $-9$ satisfy both conditions: $ {-4} + {-9} = {-13} $ $ {-4} \times {-9} = {36} $ $(x {-4}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x -9) = 0$ $x - 4 = 0$ or $x - 9 = 0$ Thus, $x = 4$ and $x = 9$ are the solutions.